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# Empirical Rule in Normal Distribution

5 The following table gives the number of homes runs hit by the American League
home-run champions for the years 1949 to 1987, given in chronological order
beginning with 1949 and proceeding left to right across the rows. (Source:
Time Almanac 2004, page 1010.)

43 37 33 32 43 32 37 52 42 42 42 40 61
48 45 49 32 49 44 44 49 44 22 37 32 32
36 32 39 46 45 41 22 39 39 43 40 40 49

a. Find the mean and standard deviation of number of home runs hit by the
American League home-run champions during the years given in the table.
Column1

Mean 40.35897436
Standard Error 1.237344671
Median 41
Mode 32
Standard Deviation 7.727214993
Sample Variance 59.70985155
Kurtosis 0.969910322
Skewness -0.149774862
Range 39
Minimum 22
Maximum 61
Sum 1574
Count 39

The mean for the number of home runs hit by the American League home-run champions is 40.358974
The standard deviation for the number of home runs hit by the American League home-run champions is 7.727215

b. Assuming that the data are approximately normally distributed, use the
empirical rule to find an interval of values within which approximately 68
percent of the data falls. Count the number of data values that actually fall
within that interval. Is it close to 68 percent?

c. Use the empirical rule to find the interval of values within which approximately
95 percent of the data falls. Count the number of data values that actually
fall within that interval. Is it close to 95 percent?
d. Use the empirical rule to find the interval of values within which approximately
99.7 percent of the data falls. Count the number of data values that actually
fall within that interval. Is it close to 99.7 percent?

#### Solution Summary

The solution provides step by step method for the calculation of mean, standard deviation and the application of empirical rule in normal distribution. Formula for the calculation and Interpretations of the results are also included.

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